Problem: On a Cartesian coordinate plane, points $(2,1)$ and $(3, 4)$ are adjacent points on a square. What is the area of the square?
Answer: We use the distance formula to find the distance between the two points, which is the side length of the square.
$\sqrt{(3-2)^2+(4-1)^2}=\sqrt{1+9} = \sqrt{10}$. Therefore, the area of the square is $(\sqrt{10})^2 = \boxed{10}$.